Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62862 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62888 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6906 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,19)(18,21)(22,23)(24,25)(26,32)(27,40)(28,29)(30,31)(33,41)(34,36)(35,44)(37,46)(38,42)(39,51)(43,45)(47,50)(48,52)(49,53);(14,15,17,19)(16,18,21,20)(23,29)(24,31)(26,38)(33,40)(35,46)(36,43)(39,50)(49,52);(14,15)(16,18)(17,19)(20,21)(22,24)(23,30)(25,29)(26,34)(27,35)(28,31)(32,43)(33,44)(36,42)(37,40)(38,45)(39,48)(41,46)(47,52)(49,51)(50,53);(14,16,17,21)(15,18,19,20)(22,25,28,30)(23,31,29,24)(26,36,38,43)(27,37,41,44)(32,45,42,34)(33,46,40,35)(39,49,50,52)(47,53,51,48);(22,26,28,38)(23,32,29,42)(24,34,31,45)(25,36,30,43)(27,39,41,50)(33,47,40,51)(35,48,46,53)(37,49,44,52);(22,27)(23,33)(24,35)(25,37)(26,39)(28,41)(29,40)(30,44)(31,46)(32,47)(34,48)(36,49)(38,50)(42,51)(43,52)(45,53)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55876);